Question

The length of a rectangle is 2m more than the width. The area of the rectangle is 20 m^2. Find the dimensions of the rectangle, to the nearest tenth of a metre.

Answer 1

The answer is w = 3.6 m, l = 5.6 m

The length (l) of a rectangle is 2m more than the width (w): l = w + 2
Area of a rectangle is: A = l * w = 20 m²

l = w + 2
l * w = 20
______
(w + 2) * w = 20
w² + 2w = 20
w² + 2w - 20 = 0

This is the quadratic function.
ax² + bx + c = 0
a = 1
b = 2
c = -20


$w_{1,2} = \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a} =\frac{-2+/- \sqrt{ 2^{2}-4*1(-20) } }{2*1} = \frac{-2+/- \sqrt{4+80} }{2} = \\ \\ = \frac{-2+/- \sqrt{84} }{2} = \frac{-2+/- 9.16 }{2} \\ \\ w_1 = \frac{-2+ 9.16 }{2}= 3.58 \\ w_1 = \frac{-2- 9.16 }{2}= -5.58$

SInce width cannot be negative: w = 3.58 ≈ 3.6 m
Thus, l = w + 2 = 3.6 + 2 = 5.6 m